## Half Life and Decay of Radioisotopes

All decay processes result from energy changes that eventually result in the formation of a stable nucleus. For example, thorium decays to radium, which decays to actinium, which eventually produces non-radioactive lead 208. The unstable nucleus releases excess energy by one or more of these processes according to characteristic rates. All radioisotopes follow the same law of decay: a fixed fraction of the atoms present will decay in a unit of time. That is, for each isotope there is a period of time during which half of the atoms initially present will decay (Table 11.21.1). Each radioactive element has a constant speed of decay, so that each element can be characterized by the time it takes for half of the element to decay. This is called the half-life of the element. Some elements decay in seconds while others take thousands of years. Since the rate of radioactive decay is not dependent on physical variables such as temperature or pressure, the half-life of each radioisotope is constant. Specific activity relates the half-life of an element to its mass, and is conventionally used to characterize radionuclides.

The specific activity (SpA) of a radioisotope is the activity per gram of the pure radioisotope. The number of atoms of a pure radioisotope in one gram (N) is given by

Na A

where:

Na = Avogadro's number (6.0248 X 1023)/nuclidic mass A = nuclidic mass

The specific activity (SpA) of a particular radioisotope is:

SpA (disintegration/sec)

0.693 Na

1.128 X 101

where:

T1/2 = half-life of the radioisotope in sec.

U-238 series

218 85At

214Pb * b b , 2]3Bi ^ a 99.96% y \19.7 m a , 214 84Po^ ^2ä°Tl * b 1.6 ¥ 10-4 s \ / 1.32 m

21820Pb * b < 20.4 y b , 283Bi * a ~100% J \5.01 d a , 210 84P°^ ^ 2|jfTl * b 138 d \ / 4.19 m

U-235 series

23925U * a

< 3.25 ¥ 104 y b , 227Ac * a 98.8% J \21.6 y a , 227 „„Th ^ 223Fr * b

b , 2J|Po * a 5 ¥ 10-4 % / \j.78 ¥ 10-3 s a , 215 85a/ ^ 281Pb * b 10-4 s \ y 36.1 m b , ^f* a 99.7% J \2.16 m a , 211 84Po^ ^ 2îjiTI * b

207Pb

Th-232 series

22888Ra * b

22898Ac * b

22908Th * a

22884Ra * a

28206Rn * a

0.014% / \0.14 s a , 216 85At^ ^ 282Pb * b 3 ¥10-4 s \ y 10.6 h b , ^b/* a 66.3% / \ 60.6 m a , 211 84Po^ ^ 2îjiTI * b 3.0 ¥ 10-7 s \ / 3.10 m

206Pb

82Pb

FIG. 11.21.2 Emissions and mission, from R.C. Weast, ed. aThe abbreviations are y, year; d half-lives of members of radioactive series. (Reprinted, with per-1978. Handbook of chemistry and physics. CRC Press, Inc.) , day; m, minute; and s, second.

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